Assumption 1 (Conditions on the Consensus Weights [1]}, [2]}) 
The consensus matrix \(\Lambda ^{(k)}=[\lambda ^{(k)}_{m,m^{\prime }}]_{m,m^{\prime }\in \mathcal {M}^{(k)}}\)  satisfies the following properties: (i) \(\lambda ^{(k)}_{m,m^{\prime }}=0~~\textrm {if}\)  there is no connection between ESs \(m\)  and \(m^{\prime }\) , (ii) \(\Lambda ^{(k)}\textbf {1} = \textbf {1}\) , (iii) \(\Lambda ^{(k)} = \Lambda ^{(k),\top }\) , and (iv) \( \rho \left(\Lambda ^{(k)}-\frac{\textbf {1} \textbf {1}^\top }{|\mathcal {M}^{(k)}|}\right) \le \lambda ^{(k)} < 1\) , where \(\textbf {1}\)  is the vector of 1s and \(\rho (\mathbf {A})\)  is the spectral radius of matrix \(\mathbf {A}\) .

